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Exercise 15 - Chapter 1

edited July 2018 in Exercises

Consider the partition [ [11 12] [13] [21] [22 23] ]

Write down every pair (a, b) such that a ∼ b. There should be 10.

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Definition 1.14 Let a, b ∈ A be elements. Given a partition, we define a relation with infix notation ∼, where a ∼ b iff a and b are in the same part.

Comments

  • 1.

    6 of the pairs are the identities \((x,x)\). The other four are due to the partitions with two elements each.

    \((11,11),(12,12),(13,13),(21,21),(22,22),(23,23), \\ (11,12),(12,11), \\ (22,23),(23,22)\)

    Comment Source:6 of the pairs are the identities \\((x,x)\\). The other four are due to the partitions with two elements each. \\((11,11),(12,12),(13,13),(21,21),(22,22),(23,23), \\\\ (11,12),(12,11), \\\\ (22,23),(23,22)\\)
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